Question

Please help with this! I've been struggling for a bit

Answer 1

29 degrees

Explanation:

Secants FH and LH form an angle at H and two intercepted arcs, FL and GJ.

By circle's theorem:

Therefore:

`m\angle H=(1)/(2)(m\widehat{FL}-m\widehat{GJ})`

Substitute the known angles:

`15\degree=(1)/(2)(59\degree-m\widehat{GJ})`

We solve the equation for the measure of arc GJ.

`\begin{gathered} \text{ Multiply both sides by 2} \\ 15*2=59-m\widehat{GJ} \\ 30=59-m\widehat{GJ} \\ m\widehat{GJ}=59-30 \\ m\widehat{GJ}=29 \end{gathered}`

The measure of arc GJ is 29 degrees.